Question edited on 27.06.2018 for clarity The Cosmic Microwave Background (CMB) is often called the radiation leftover from big bang, or more precisely, the photons decoupled from the thermal bath when the first atoms were formed.

When we measure the radiations i.e., the flux of photons in a given microwave range (say, 0.1cm to 70cm, for example), in deep sky, there are radiations coming from different galactic sources. When one carefully eliminates photon contributions from these sources and then makes a plot of the intensity versus frequency, one obtains a curve that mimics a blackbody (BB) radiation spectrum. Using that one estimates the temperature to be around $2.7$K.

Back in the time when the universe was younger, this background radiation had a much higher temperature. Then it eventually cooled down with the expansion of the universe to the temperature $2.7$K.

Question

$\bullet$ But apart from being affected by the expansion of the universe, shouldn't the CMB photons be continually contaminated by various luminous sources in the galaxy? Do we have any reason to think that galaxies don't emits photons of microwave range and mix with CMB photons? If yes, they are not really the old photons that were decoupled in the early Universe, and it seems impossible to separate the photons CMB from other microwave radiations that are probably mixing with it.

$\bullet$ Also, what is the reason to think that those old photons have survived till today since decoupling in spite of being (perhaps) continually absorbed by the interstellar medium?

$\bullet$ It is assumed that CMB photons are affected only by expansion. How is it possible that this CMB exists without any interaction with other photons coming from stars etc? Photons can interact with photons at the higher order in QED perturbation theory even though the probability of interaction is highly suppressed.

2 Answers
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Yes, the CMB could be partially absorbed by dust or other galaxies that are now in front of it, however, since we know the spectrum should be a black body spectrum. We can, for a certain point on the sky, measure the CMB at various wavelengths and see what temperature black body spectrum would fit this data best. Thus people can make these famous maps where you see the temperature of the CMB radiation fluctuate slightly at various points in the sky. Even though there is indeed quite some noise on top of the CMB signal nowadays we can filter out the noise since the noise itself doesn't typically follow a black body spectrum with the same temperature as the rest of the CMB.

But how can we be sure most of what we see on these maps is actual signal rather than noise? From calculations which predict the distribution of elements in the universe one can show that the amount of photons that was emitted as this leftover radiation was so intense that in the early universe (when the CMB still had a black body spectrum of $T=10000K$ instead of the current $T=2.7K$) all energy from the CMB was so intense that it dominated the total energy content of the entire visible universe. Try to imagine that! An enitre Universe, filled with radiation of thousands of degrees.

This makes us pretty confident that the couple of photons emitted or absorbed after the initial emission of the CMB doesn't change the main results. Though there is a whole branch of physics specializing in removing the noise to observe smaller and smaller structures of the CMB.

$\begingroup$@JgL- But how is it possible to separate the photons CMB radiation from other microwave radiations? How is it possible that this CMB exists without any interaction with other photons coming from stars etc.? I find it very difficult to digest that the CMB is stable (i.e., never interact with other photons) except the CMB photons are being stretched in wavelength with the expansion of the universe?$\endgroup$
– SRSJan 23 '15 at 15:37

$\begingroup$"" without any interaction with other photons coming from stars etc.?"" What makes You think that photons do interact with other photons?$\endgroup$
– GeorgJan 23 '15 at 15:44

$\begingroup$@ Georg- In J. D. Jackson's classical electrodynamics, he argued that in QED $\gamma(p_1)+\gamma(p_2)\rightarrow \gamma(k_1)+\gamma(k_2)$ is possible. The corresponding Feynman diagram is also given. Therefore why not CMB photon can interact with ordinary photons? Is this because these processes appear at higher order in perturbation and therefore the probability of interaction is highly suppressed?$\endgroup$
– SRSJan 24 '15 at 13:45

$\begingroup$In QED it is indeed possible for photons to interact due to interactions with 'virtual' electrons, this however is quite a negligible effect. Especially when compared to the vast number of CMB photons that have an almost perfect black body spectrum there is no reason to believe that this peak at a specific wavelength arose from such $\gamma\gamma$ scattering. Furthermore, there is other independent evidence, like the distribution of elements in the early universe that points to the same conclusion of the Universe being very hot in an earlier stage, predicting the correct CMB wavelength.$\endgroup$
– JgLFeb 20 '15 at 14:12

But apart from being affected by the expansion of the universe, shouldn't the CMB photons be continually contaminated by various luminous sources in the galaxy?

So luminous sources of microwave radiation are localized to galaxies and their stars and can be eliminated. Electromagnetic radiation travels in straight lines, and the probability of a photon hitting a dust particle and "contaminating" the primordial signal would contribute to systematic errors the study of errors are ongoing research,for example here.

Also, what is the reason to think that those old photons have survived till today since decoupling in spite of being (perhaps) continually absorbed by the interstellar medium?

Decoupling means that there are no interactions . The intergalactic medium density is very low, order of 1 hydrogen atom per meter cubed to 1 atom per $cm^3$, whereas microwave radiation comes as light, i.e. zillions of photons.

It is assumed that CMB photons are affected only by expansion. How is it possible that this CMB exists without any interaction with other photons coming from stars etc